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In order to propose a statistical methodology that allows to model asymmetric data using the Lévy distribution, a simulation study is presented under nine different scenarios to evaluate the estimation of the parameters of the distribution in the two approaches of statistics (Classical and Bayesian). The probability distributions Log-Normal, Lévy and Lévy Standard were considered to model the behavior of two real data sets with positive asymmetry, finding that the Lévy distribution fitted well to the proposed data set, therefore the Lévy distribution can be considered as a candidate to adjust asymmetric data with the presence of extreme values. [ABSTRACT FROM AUTHOR]

A class of estimators is determined. It contains important families of ratio estimators. The belonging to it is characterized by means of a parametric vector. It allows identifying that more than a dozen of estimators are particular cases. Their behavior when ranked set sampling is used is established by fixing the gains in accuracy of them. Numerical experiments establish which is the performance of them in four applications and by generating normal, exponential and uniform populations. [ABSTRACT FROM AUTHOR]